Popular tomographic imaging techniques include x-ray computed tomography (CT). Particularly in view of potentially harmful effects of CT scans, a recent trend in CT research is the development of imaging techniques which allow for reducing the radiation dose applied to the imaged object, e.g. the body of a patient or part thereof. One related approach involves the reduction of the numbers of projections measured during a CT scan. This can be achieved using the so-called sparse angular sampling technique. In accordance with this technique, projections are acquired only at a number of angular sampling positions, which is selected as small as possible. Hereby, the radiation dose applied to the object can be reduced. Moreover, the acquisition time for acquiring the image can be reduced so that sparse angular sampling can also be advantageously applied in other tomographic imaging techniques, where the sparse angular sampling technique does not result in a reduction of the radiation dose applied to the object, such as Magnetic Resonance Imaging (MRI) and Single-Photon Emission Computed Tomography (SPECT).
In sparse angular sampling, the angular sampling positions are usually selected such that neighboring angular sampling positions have a constant angular distance. Such a selection is optimal in case the object contour is approximately rotation-symmetric with respect to the axis (z-axis) of the tomographic scanner. However, in case of on an asymmetric object contour and/or in case the object is positioned off-center in the examination region of the tomographic scanner, a constant angular distance between the sampling positions leads to an undesired variation of the sampling density (i.e. the number of measured radiation rays through a volume element which correspond to the number of projection lines through a volume element in x-ray CT) within the object. This is due to the fact that the sampling density decreases with an increasing distance from the z-axis. As result, the sampling density in outer object regions having a larger distance to the z-axis (e.g. regions where the object has a larger radial extension) is smaller than the sampling density in outer object regions which have a smaller distance to the z-axis (e.g. region where the object has a smaller radial extension).
Such a variation of the sampling density may lead to an over-sampling of object regions with a higher sampling density (i.e. regions having a smaller distance to the z-axis) or an under-sampling of object regions with a lower sampling density (i.e. regions which have a larger distance to the z-axis), where an over-sampling contravenes the aim of the sparse angular sampling technique and where an under-sampling leads to undesired artifacts in the tomographic images.
A. Dogandzic et. al disclose, in “Mask Iterative Hard Thresholding Algorithms for Sparse Image Reconstruction of Objects with Known Contour”, arXiv.org, Cornell University Library, 2 Dec. 2011, that by exploiting both the geometric contour information of the underlying image and sparsity of its wavelet coefficients, a CT image can be reconstructed with a reduced number of measurements.
H. Kudo et. al, reviews, in “Image reconstruction for sparse-view CT and interior CT—introduction to compressed sensing and differentiated backprojection”, Quant. Imaging Med. Surg., vol. 3, 1 Jan. 2013, pages 147-161, mathematical principles of the compressed sensing image reconstruction and the differentiated backprojection image reconstruction for sparse-view CT.